Problem: What do the following two equations represent? $-4x-y = 4$ $3x-12y = -3$
Explanation: Putting the first equation in $y = mx + b$ form gives: $-4x-y = 4$ $-y = 4x+4$ $y = -4x - 4$ Putting the second equation in $y = mx + b$ form gives: $3x-12y = -3$ $-12y = -3x-3$ $y = \dfrac{1}{4}x + \dfrac{1}{4}$ The slopes are negative inverses of each other, so the lines are perpendicular.